An Upper Bound on the Maximum Stability Radius Achievable by State Feedback

2005 ◽  
Vol 128 (3) ◽  
pp. 718-721 ◽  
Author(s):  
R. Rajamani ◽  
Y. M. Cho
Keyword(s):  
Upper Bound ◽  
State Feedback ◽  
Closed Loop ◽  
Stability Radius ◽  
Feedback Matrix ◽  
Maximum Stability ◽  
Loop Matrix ◽  
The Stability

In this paper we relate the stability radius that can be achieved for the closed-loop matrix (A−BK) to the distance to unstabilizability of the pair (A,B). In the paper we show that the closed-loop matrix (A−BK) can achieve a stability radius of γ with a real feedback matrix K only if the distance to unstabilizability of (A,B) is greater than γ. Thus the distance to the unstabilizability of (A,B) provides an upper bound on the maximum stability radius that can be achieved by state feedback.

scholarly journals Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

2018 ◽  
Vol 41 (1) ◽  
pp. 285-294
Author(s):  
Akshata Tandon ◽  
Amit Dhawan ◽  
Manish Tiwari
Keyword(s):  
Cost Function ◽  
Upper Bound ◽  
State Feedback ◽  
Closed Loop ◽  
Roesser Model ◽  
Memory State ◽  
Delayed Systems ◽  
Discrete State ◽  
Guaranteed Cost ◽  
Memory State Feedback

This paper is concerned with the problem of optimal guaranteed cost control via memory state feedback for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the Roesser model with norm-bounded uncertainties. A linear matrix inequality (LMI)-based sufficient condition for the existence of memory state feedback guaranteed cost controllers is established and a parameterized representation of such controllers (if they exist) is given in terms of feasible solutions to a certain LMI. Furthermore, a convex optimization problem with LMI constraints is formulated to select the optimal guaranteed cost controllers that minimize the upper bound of the closed-loop cost function. The proposed method yields better results in terms of least upper bound of the closed-loop cost function as compared with a previously reported result.

Robust H∞ State Feedback Control With Regional Pole Constraints: An Algebraic Riccati Equation Approach

1998 ◽  
Vol 120 (2) ◽  
pp. 289-292 ◽  
Author(s):  
Zidong Wang
Keyword(s):  
Riccati Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
State Feedback Control ◽  
Algebraic Riccati Equation ◽  
Equation Approach ◽  
Parameter Uncertainties ◽  
Realization Problem ◽  
Loop Matrix

This paper focuses on the controller design for uncertain linear continuous-time systems with H∞ norm and circular pole constraints and addresses the following multiobjective simultaneous realization problem: designing a state feedback controller such that the closed-loop system, for all admissible parameter uncertainties, simultaneously satisfies the prespecified H∞ norm constraint on the transfer function from disturbance input to output and the prespecified circular pole constraint on the closed-loop matrix. An effective, algebraic, modified Riccati equation approach is developed to solve this problem. The existence conditions, as well as the analytical expression of desired controllers, are derived. A numerical example is provided to show the directness and effectiveness of the present approach.

ON THE STABILITY RADIUS OF SWITCHED POSITIVE LINEAR SYSTEMS

2020 ◽  
pp. 90-98
Author(s):  
Ngoc
Keyword(s):  
Lower Bound ◽  
Linear Systems ◽  
Upper Bound ◽  
Lyapunov Functional ◽  
Stability Radius ◽  
Exponentially Stable ◽  
The Stability

This article investigates the stability radius based on exponentially stable of switched positive linear systems. A lower bound and upper bound for this radius with respect to structured affine positive perturbations of the system's parameters are established under the assumption that all its positive subsystems have a common linear copositive Lyapunov functional. An example is provided for illustrating the result.

Stable observer-based controller design for robust state-feedback pole assignment

2000 ◽  
Vol 214 (4) ◽  
pp. 313-318 ◽  
Author(s):  
G P Liu ◽  
G R Duan ◽  
S Daley
Keyword(s):  
Frequency Domain ◽  
Stability Problem ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Pole Assignment ◽  
Loop System ◽  
Closed Loop System ◽  
Sensitive Function ◽  
The Stability

The design of stable observer-based controllers for robust pole assignment is addressed in this paper. The stability problem of these dynamical controllers is investigated, which is often ignored during the controller design. A design formulation of stable observer controllers is presented using state-feedback pole assignment techniques. Although the design formulation is principally aimed at the design of a stable controller, the mixed sensitive function in the frequency domain is also considered to improve the robustness of the closed-loop system. This ensures that the closed-loop system has good robustness and the controller is stable.

CHAOTIC CONTROL AND CHAOTIFICATION USING FUZZY APPROACH

2008 ◽  
Vol 18 (01) ◽  
pp. 263-274
Author(s):  
KUANG-YOW LIAN ◽  
CHENG-SEA HUANG ◽  
WEN-HSIEN FANG ◽  
CHIEN-HSING SU
Keyword(s):  
State Feedback ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Feasible Solution ◽  
Fuzzy Model ◽  
Stabilization Problem ◽  
Unified Approach ◽  
Closed Loop System ◽  
Chaotic Control ◽  
The Stability

In this paper, we propose a fuzzy model-based methodology to deal with various control objectives for discrete-time chaotic systems from a unified viewpoint. With intent to unify the design process, we introduce a new design concept called virtual-desired-variable synthesis. Then, both the chaotic control and chaotification are eventually treated as a stabilization problem. Consequently, the conditions concerning the stability of the closed-loop system are formulated into LMIs. A feasible solution of the LMI problem guarantees the quadratical stability and gives the state feedback gains as well. The well-known Hénon map is used to demonstrate the unified approach.

A simulation apparatus for the experimental study of batch reactor control methods

1986 ◽  
Vol 51 (6) ◽  
pp. 1259-1267
Author(s):  
Josef Horák ◽  
Petr Beránek
Keyword(s):  
Experimental Study ◽  
Closed Loop ◽  
Dynamic Properties ◽  
Batch Reactor ◽  
Exothermic Reaction ◽  
Electric Heating ◽  
Batch Reactors ◽  
Exchange Area ◽  
The Stability ◽  
Methods Of Control

A simulation apparatus for the experimental study of the methods of control of batch reactors is devised. In this apparatus, the production of heat by an exothermic reaction is replaced by electric heating controlled by a computer in a closed loop; the reactor is cooled with an external cooler whose dynamic properties can be varied while keeping the heat exchange area constant. The effect of the cooler geometry on its dynamic properties is investigated and the effect of the cooler inertia on the stability and safety of the on-off temperature control in the unstable pseudostationary state is examined.

Adaptive attitude-tracking control of spacecraft considering on-orbit refuelling

2020 ◽  
pp. 014233122097313
Author(s):  
Yiqi Xu
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Closed Loop System ◽  
Tracking Errors ◽  
Attitude Tracking ◽  
Control Scheme ◽  
Inertia Model ◽  
And Performance ◽  
Attitude Tracking Control ◽  
The Stability

This paper studies the attitude-tracking control problem of spacecraft considering on-orbit refuelling. A time-varying inertia model is developed for spacecraft on-orbit refuelling, which actually includes two processes: fuel in the transfer pipe and fuel in the tank. Based upon the inertia model, an adaptive attitude-tracking controller is derived to guarantee the stability of the resulted closed-loop system, as well as asymptotic convergence of the attitude-tracking errors, despite performing refuelling operations. Finally, numerical simulations illustrate the effectiveness and performance of the proposed control scheme.

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